Method for detecting mobile objects with active sonar

ABSTRACT

A process for making it possible to detect moving objects by an active sonar operating by the Dopper effect. The process uses, as a transmission signal, a burst of N pulses encoded so as to present a spectrum having a comb-of-lines structure. In this way, the “signal/reverberation” ratio of the useful signal intensity to the reverberated intensity is increased, thereby increasing the efficiency of the sonar. The process allows objects moving in a reverberating transmission medium to be detected more easily.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to processes for detecting movingunderwater objects by means of an active sonar, comprising a directionalantenna, by using the Doppler effect attached to the relative movementof the object and of the sonar and by forming directional channels onthe basis of the signals from the transducers of the antenna.

2. Discussion of the Background

In order to detect a moving object, called, target a with a sonar, it isknown practice to use the Doppler effect produced by the movement of thetarget. In such processes of the prior art, a pulse of narrow bandwidthcompared with the Doppler shift from the target is transmitted, then onreception, the received signals are simultaneously correlated withseveral frequency-shifted copies of the transmitted pulse. Eachcorrelation copy corresponds to a different possible Doppler shift. Thebest correlation is obtained with a copy having a frequency shiftapproximately equal to that caused by the movement of the target. Thus,the correlation by many copies and the use of the signals received makeit possible to locate a target by distance and by azimuth and tocalculate its radial velocity.

This process amounts to transmitting a bandwidth code which is narrowerthan the Doppler shift from the targets that one is seeking to detect.To do this, the transmission consists of a pulse of pure frequency f₀and duration T, amplitude-weighted in order to reduce the level of thesecondary lobes of the spectrum transmitted so as to obtain goodspectral rejection. The spectral width of such a pulse is then about 4/Tfor a cos² weighting.

It is known that the marine environment is reverberant, especiallybecause of the many local heterogeneities (air bubbles, particles,plankton, etc.) forming scatterers. In addition, at shallow depths, thereverberation coming from the bottom and from the surface issignificant. It follows that, when the spectrum of the reverberatedsignal and the spectrum of the copy are superimposed in the angularsector corresponding to the main lobe of the antenna, the detectionperformance is very poor.

FIG. 1 shows the value of the frequency f of the signal received as afunction of the cosine of the angle θ between the velocity vector of thesonar carrier and the direction of a point in space in the bearingplane.

As the carrier moves with a uniform velocity V and as the transmittedfrequency is f₀, it is known that the received frequency is given by(1+2|V|/c cos θ)f₀ where c is the speed of the acoustic waves in thewater. The spread of the spectrum of the signal reverberated by theentire volume subjected to the sound is therefore represented by asloping straight line 101 of width 4/T. As to the copy, this isindependent of θ and is shown by a vertical straight line 102 of width4/T.

The region denoted A corresponds to the reverberation case indicatedabove. In this region, the reverberated signal is received in the mainreceiving lobe 103. It is not removed either by the directivity, nor bythe Doppler filtering.

The regions denoted B correspond to the case in which the spectrum ofthe reverberated signal and that of the copy are superimposed oppositethe secondary lobes 104 of the receiving channel. There are thereforetwo contributions to the reverberated intensity detected. The first isthat of the scatterers in the main lobe of the receiving channel, but atfrequencies different from the target. These scatterers are rejected byspectral analysis. As the latter can reach 40 to 50 dB in sonar, thiscontribution can be ignored. A second contribution corresponds to thescatterers at the same frequency as the target, but attenuated by thesecondary lobes of the directivity pattern. The situation in the figureshows the intersection 105 of the straight lines 101 and 102 with thesecondary lobe 106.

The “reverberation/signal” ratio is given by the formula:$\begin{matrix}{R{.2}{\Delta\theta}\frac{c\quad T}{2}{.10}^{- \frac{N\quad S}{10}}} & (1)\end{matrix}$

where R is the distance from the target and NS is the level in dB of thesecondary lobes of the directivity pattern.

The angular interval Δθ corresponding to the spectral overlap betweenthe copy and the reverberated signal is such that Δ cos θ=λ/VT and theratio (1) does not depend on the duration T of the transmitted pulse:the fact of increasing this duration would not allow the performance tobe increased.

The regions denoted C correspond to the case in which there is noscatterer at the frequency of the receiving channel. In this case, theperformance is generally very good, but it only corresponds to a limitednumber of potential targets.

Patent application Ser. No. 92/01499, filed on Feb. 11, 1992 by theThomson-CSF company and published on Aug. 13, 1993 under U.S. Pat. No.2,687,226 describes a process for detecting moving targets in which aseries of pulses at pure frequencies is transmitted. Its drawbacks stemfrom the fact that the performance in regions B remain poor and that thetransmitted frequencies depend on the speed of the target.

SUMMARY OF THE INVENTION

In order to be able to obtain good performance equally in the A and Bregions, while retaining the performance of the C regions, the inventionproposes a process for detecting moving objects by an active sonarmoving at a velocity V, in which a signal of duration T is transmitted,which signal is reverberated by the transmission medium, presenting aspectral spread due to the actual speed of the sonar and thisreverberated signal is processed by correlation with a set of thefrequency-shifted copies of the transmission signal in order tocorrespond to the set of Doppler shifts capable of affecting thereverberated signal, mainly characterized in that the transmitted signalis broadband encoded in order to present a spectrum having acomb-of-lines structure at successive frequencies f_(i), the intervalseparating two successive lines f_(i) and f_(i+1) of which is a functionof the velocity V in order to be at least equal to the spectrum spreadby satisfying the formula:${{\left( {1 - \frac{2V}{c}} \right)f_{i + 1}} - \frac{a}{T}} \geq {{\left( {1 + \frac{2V}{c}} \right)f_{i}} + \frac{a}{T}}$

where a is an integer between 1 and 2.

According to another characteristic, the encoded signal is formed by Npulses, each of which occupies a frequency band B centered on afrequency f₀, where N is greater than or equal to:$N \cong {\frac{4V\quad T}{c}{\left( {f_{0} + \frac{B}{2}} \right).}}$

According to another characteristic, the transmission signal furthermorecomprises two pulses at pure frequences f_(m) and f_(M) intended to makeit possible to detect fast moving objects, the echoes from which arelocated beyond the frequency band occupied by the reverberated signalboth when receding and when approaching, these frequencies being givenby the equations:${{\left( {1 + \frac{2V}{c} + \frac{2{V_{c}^{\max}}}{c}} \right)f_{m}} + \frac{2}{T}} \leq {{\left( {1 - \frac{2V}{c}} \right)f_{1}} - {\frac{2}{T}\quad {{and}\left( {1 + \frac{2V}{c}} \right)}f_{1}} + \frac{2}{T}} \leq {{\left( {1 - \frac{2V}{c} + \frac{2{v_{c}^{\max}}}{c}} \right)f_{M}} - {\frac{2}{T}.}}$

According to another characteristic, in order for the moving objects,whose speed is approximately equal to one of the blind speeds of thebroadband encoded signals, to be detected by the pure-frequency signals,the frequencies f_(m) and f_(M) are chosen to satisfy, in addition, theequations:$f_{M} = {{q\frac{N}{T}\quad {and}\quad f_{m}} = {\left( {p \pm \frac{\Delta}{2}} \right)\frac{N}{T}}}$

where Δ corresponds to the smallest interval separating the arithmeticseries of the p/q ratio from the series of integers.

According to another characteristic, a process is used in which f_(m)and f_(M) are chosen so as to satisfy the equations:$\left\{ \begin{matrix}{{{\left( {1 + \frac{2V}{c}} \right)f_{1}} + \frac{2}{T}} \leq {{\left( {1 - \frac{2V}{c} - \frac{2{V_{c}^{\max}}}{c}} \right)f_{m}} - \frac{2}{T}}} \\{{{\left( {1 + \frac{2V}{c}} \right)f_{1}} + \frac{2}{T}} \leq {{\left( {1 - \frac{2V}{c} - \frac{2{V_{c}^{\max}}}{c}} \right)f_{M}} - \frac{2}{T}}}\end{matrix} \right.$

According to another characteristic, a process is used in which f_(m)and f_(M) are chosen so as to satisfy the equations:$\left\{ \begin{matrix}{{{\left( {1 + \frac{2V}{c} + \frac{2{V_{c}^{\max}}}{c}} \right)f_{m}} + \frac{2}{T}} \leq {{\left( {1 - \frac{2V}{c}} \right)f_{M}} - \frac{2}{T}}} \\{{{\left( {1 + \frac{2V}{c} + \frac{2{V_{c}^{\max}}}{c}} \right)f_{M}} + \frac{2}{T}} \leq {{\left( {1 - \frac{2V}{c}} \right)f_{1}} - \frac{2}{T}}}\end{matrix} \right.$

According to another characteristic, a towed linear acoustic antenna isused to receive the reverberated signals.

BRIEF DESCRIPTION OF THE DRAWINGS

Other particular features and advantages of the invention will becomeclearly apparent in the following description, presented by way ofnonlimiting example, with reference to the appended figures which show:

FIG. 1, a frequency/direction diagram for a signal transmitted at a purefrequency;

FIG. 2, a diagram similar to that of FIG. 1, but corresponding to aburst of N signals;

FIG. 3, a similar diagram corresponding to the transmission at two purefrequencies; and

FIG. 4, a diagram similar to that of FIG. 2, of N signals transmitted inaccordance with the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The invention proposes to use encoded signals according to codes forwhich the spectrum has a so-called called comb-of-lines structure.

Such a structure can be obtained by transmitting a periodic broadbandsignal, or by direct synthesis in the spectral domain. Let us suppose,for example, that the transmitted code consists of N identicalcos²-weighted “subcodes” or broadband (FM, BPSK or other) “elementarypatterns”, each one of duration T/N, the whole sequence beingamplitude-weighted over the duration T. Its spectrum, shown in afrequency/direction diagram as in FIG. 1, will then have the appearanceshown in FIG. 2. The comb-of-lines 201, each one of width 4/T (betweenthe first zeroes), separated by N/T, and having a strong spectralrejection between the lines, can be seen. The set of lines covers abandwidth B.

By considering a copy 202, shifted in frequency for detection, manyangular directions 206, 216, 226 contributing to the cross spectrumbetween the copy and the reverberation are found in region B. By takingas variable u=cos θ, these various directions are separated by Nλ/2VT.As the variable u varies from −1 to +1, the number of these directionsis given by the formula: $\begin{matrix}{M = \frac{4V\quad T}{N\quad \lambda}} & (2)\end{matrix}$

In this region B, the ratio of the reverberated intensity to thetransmitted energy is approximately equal to: $\begin{matrix}{R\frac{4V_{c}^{\max}T}{\lambda}\lambda \quad \theta_{0}\frac{c}{2B}{.10}^{\frac{- N_{s}}{10}}} & (3)\end{matrix}$

where:

V_(c)=radial velocity of the target

Δθ₀=angular interval of overlap of the spectra.

This formula is valid when V_(c) ^(Max)≧2V, which is almost always thecase in practice.

If this formula is compared to formula (1), which was set up for thepure-frequency mode called “PF” mode, a performance gain G is obtained,equal to: $\begin{matrix}{G = \frac{c\quad B}{2V_{c}^{Max}f_{0}}} & (4)\end{matrix}$

With a bandwidth equal to one third of the carrier frequency and avelocity V_(c) ^(Max)=30 knots, a gain of 9.2 dB is obtained. The gainis lower, the higher the velocity V_(c) ^(Max).

If V_(c) ^(Max)<2V, the value of G is$\frac{c\quad B}{4V\quad f_{0}}$

Thus, for V=10 knots and B/f₀=1/3, G=14 dB.

The invention therefore proposes to use a comb-of-lines broadband codematched to the velocity of the carrier, independently of the speed ofthe target.

This broadband code, of duration T and of bandwidth B, is such that thespacing between each line of its spectrum is equal to the reverberationfrequency spread associated with the line originating solely from thevelocity V of the carrier, as shown in FIG. 3, where the width of thepulses 301 has been exaggerated compared to the variation interval 300of the copy.

For 2 adjacent lines, this condition can be written: $\begin{matrix}{{\left( {1 - \frac{2V}{c}} \right)f_{i + 1}} \geq {{\left( {1 + \frac{2V}{c}} \right)f_{i}} + \frac{4}{T}}} & (5)\end{matrix}$

The diagram of the cos θ direction as a function of frequency underthese conditions is shown in FIG. 4. Note that a single reverberationdirection 306 contributes to the cross spectrum.

The broadband code used is composed of N pulses each having a band widthB centered on the frequency f₀. The interval between 2 adjacent lines issuch that f_(i+1)=f_(i)=N/T. By taking the least favorable case, thefollowing is obtained using formula (5). $\begin{matrix}{N \geq {4\left\lbrack {{\frac{VT}{c}\left( {f_{0} + \frac{B}{2}} \right)} + 1} \right\rbrack}} & (6)\end{matrix}$

The optimum situation is obtained for the equality.

In order to control the secondary loads of the transmitted spectrum,this number will preferably be greater than a minimum number, equal, forexample, to 12. This condition then corresponds to carrier velocitiesmeeting the condition: $\begin{matrix}{V \geq \frac{2C}{{Tf}_{0}}} & (7)\end{matrix}$

For the sake of simplification, this value of N=12 will be kept forlower speeds.

In formula (5), i varies from 1 to a maximum value given by:$\begin{matrix}{i_{\max} = {I = {E\left( {\frac{BT}{N} + 1} \right)}}} & (7)\end{matrix}$

where E means “integer part”.

Corresponding to these 2 values are the 2 frequencies$f_{0} - {\frac{B}{2}\quad {and}\quad f_{0}} + {\frac{B}{2}.}$

The processing on receiving this broadband code can be carried outconventionally by correlation with copies which correspond to all thepossible “Doppler targets”.

By simplifying formula (6) to:$N \cong {\frac{4{VT}}{c}\left( {f_{0} + \frac{B}{2}} \right)}$

the gain G obtained in region B compared with the PF mode is given bythe formula: $\begin{matrix}{G = {{\frac{BT}{N}\left( {1 + \frac{B}{2f_{0}}} \right)\quad {for}\quad V_{c}^{\max}} < {2V}}} & (8)\end{matrix}$

and by the formula $\begin{matrix}{G = {{2\quad \frac{BT}{N}\left( {1 + \frac{B}{2f_{0}}} \right)\frac{V}{V_{c}^{\max}}\quad {for}\quad V_{c}^{\max}} \geq {2{V.}}}} & (9)\end{matrix}$

In a preferred embodiment, the invention proposes to use twoconventional codes, PF 401 and 411, each with the same energy as thebroadband code, whose frequencies are located symmetrically with respectto the spectrum of the broadband code.

The frequencies f_(m) and f_(M) of these two codes are determined insuch a way as to detect the target, by one of the two codes, as soon asthe target is in the region C.

In order to do this, f_(m) and f_(M) must satisfy the followinginequalities: $\begin{matrix}{{{\left( {1 + \frac{2V}{c} + \frac{2{V_{c}^{\max}}}{c}} \right)f_{m}} + \frac{2}{T}} \leq {{\left( {1 - \frac{2V}{c}} \right)f_{1}} - \frac{2}{T}}} & (10)\end{matrix}$

and $\begin{matrix}{{{\left( {1 + \frac{2V}{c}} \right)f_{l}} + \frac{2}{T}} \leq {{\left( {1 - \frac{2V}{c} - \frac{2{V_{c}^{\max}}}{c}} \right)f_{M}} - \frac{2}{T}}} & (11)\end{matrix}$

The reception processing of these 2 codes will be identical to that ofthe broadband code, i.e. correlation with copies 402 and 412 whichcorrespond to the “Doppler targets” in the C regions (approaching in thecase of the f_(M) code, receding in the case of the f_(m) code).

The targets, for which the radical velocity V_(r) satisfies equation:$\begin{matrix}{{\frac{2{V_{r}}}{c}\quad f_{0}} = {k\quad \frac{N}{T}}} & (12)\end{matrix}$

where k is an integer, reflect a signal whose spectrum coincides withthat of the reverberation in the direction of the target, and thereforelie in region A, with very little chance of being detected. Thiscorresponds, as in any Doppler system, to blind frequencies.

However, these blind velocities correspond in all cases, taking intoaccount the frequency spacing chosen for the broadband code, to targetsin region C (the worst cases correspond to a target coming from the rearwith a radial velocity of 2V, or a target coming from the front with aradial velocity of −2V). It is therefore possible, according theinvention, to treat them with PF codes.

The performance in region C is therefore that of the PF mode, oncondition that the spectra of the various codes are separatedsufficiently to be able to ignore the mutual interactions.

In particular, for the “burst” codes, the various lines occupy thepositions kN/T where k is an integer, and for certain elementarypatterns (FM code for example), the decrease in the level of these linesis quite slow, so that the reverberation produced by the transmission ofthe broadband code in the PF copy can become a problem. This isparticularly so when the spectrum of the PF copy intercepts one of thespectral lines of the reverberation associated with the broadband codeopposite the main lobe of the channel pointing at the target. Thiscorresponds to a condition given by the formula: $\begin{matrix}{{{{\left( {1 + {\frac{2V}{c}\quad \cos \quad \theta_{0}}} \right)k\quad \frac{N}{T}} = {\left( {1 + {\frac{2V}{c}\quad \cos \quad \theta_{0}} + \frac{2V_{r}}{c}} \right)f_{m}}}{{{for}\quad {low}\quad {PF}},{or}}}\quad} & (13) \\{{{{\left( {1 + {\frac{2V}{c}\quad \cos \quad \theta_{0}}} \right)k^{\prime}\quad \frac{N}{T}} = {\left( {1 + {\frac{2V}{c}\quad \cos \quad \theta_{0}} + \frac{2V_{r}}{c}} \right)f_{M}}}{{for}\quad {high}\quad {{PF}.}}}{\quad \quad}} & (14)\end{matrix}$

As the value of $\frac{2V}{c}\quad \cos \quad \theta_{0}$

is small compared with 1, to a first order these equations become:$\begin{matrix}{{\left( {1 + \frac{2{Vr}}{c}} \right)f_{m}} = {k\quad \frac{N}{T}}} & (15) \\{{\left( {1 + \frac{2{Vr}}{c}} \right)f_{M}} = {k^{\prime}\quad \frac{N}{T}}} & (16)\end{matrix}$

The 2 conditions (13) and (14) can occur simultaneously, which meansthat detection of the target by one of the 2 PF codes in region C istherefore not ensured.

In order to remedy this, it is possible to set the frequency values to$f_{M} = {{q\quad \frac{N}{T}\quad {and}\quad f_{m}} = {{p\quad \frac{N}{T}} + {\delta \quad \frac{N}{T}}}}$

where q and p are integers.

The value of δ is then such that${\delta = {\pm \quad \frac{\Delta}{2}}},$

where Δ corresponds to the smallest interval separating the arithmeticseries of the p/q ratio from the series of integers.

Thus targets having a Doppler shift of less than N/T in absolute valuewill be detected by the broadband code, and other targets will bedetected by one of the PF codes.

However the invention still operates, but with degraded performance,when only one of these 2 pure frequencies is used.

In one embodiment, a sonar with a towed linear antenna whose bandwidthavailable at transmission Δf=600 Hz is centered on f₀=1500 Hz, and whichmoves at the velocity of V=4 m/s, was produced. The energy transmittedcorresponds to codes of duration T=8 s, the sound level and the desiredcarriers being taken into account.

As the band B is less than Δf, N can be obtained from (6). ThereforeN=157.6, from which N/T=19.7 Hz which can be rounded up to 20 Hz. Thusthe broadband code is formed from 160 pulses each of 50 ms duration.

For the PF codes, f_(M)=1800 Hz so q=90. Therefore f_(m)=1203.33 Hz,p=60, p/q=2/3 and Δ=1/3. From this it can be deduced that f_(m)=1203.33Hz.

The inequalities (10) and (11) lead to f₁=63×20=1260 Hz andf₁=87×20=1740 Hz. Each pulse of the broadband code therefore has a bandequal to 480 Hz.

The transmission of such a sonar can therefore be formed:

by a first amplitude-weighted PF code, of duration T=8 s (from 0 to T)and of frequency f_(m)=1260 Hz;

by an amplitude-weighted broadband code, of duration T=8 s (from T/2 to3T/2) consisting of N=160 pulses of duration 50 ms and of bandwith B=480Hz centered on 1500 Hz;

by a second amplitude-weighted PF code, of duration T=8 s (from T2 to T)and of frequency f_(M)=1800 Hz.

At reception, the following processing is then carried out:

formation of channels;

in each channel formed, matched filtering, the nature of the copies ofwhich depends on the frequency interval in question;

for the radial velocities V_(r) of the targets, such that:$\begin{matrix}{{- \frac{N}{T}} \leq {\frac{2V_{r}}{c}f_{l}} \leq \frac{N}{T}} & (18)\end{matrix}$

the copies are generated by carrying out a Doppler shift of thebroadband transmitted code with the Doppler parameters corresponding tothe interval 2N/T;

for the other velocities V_(r), such that $\begin{matrix}{{\frac{2{V_{r}}}{c}f_{l}} > \frac{N}{T}} & (19)\end{matrix}$

the copies are generated by Doppler shift of the frequencies f_(m) andf_(M) with the corresponding Doppler parameters.

The matched filtering of the received signal is carried outsimultaneously with all the copies thus generated and the knowndetection and normalization processes of the prior art are applied.

As a variant, the broadband code can be synthesized directly using thefollowing formula: $\begin{matrix}{{{e(t)} = {\sum\limits_{i = 0}^{I}{a_{i}{\cos \left( {{2\pi \quad f_{i}t} + \varphi_{i}} \right)}{{env}\left( \frac{t}{T} \right)}}}}{{in}\quad {{which}:}}} & (20) \\{{{\left( {1 - \frac{2V}{c}} \right)f_{i + 1}} = {{\left( {1 + \frac{2V}{c}} \right)f_{i}} + \frac{4}{T}}}{{{{with}\quad i} = 1};\quad {i_{\max} = {E\left( {\frac{B\quad T}{N} + 1} \right)}}}} & (21)\end{matrix}$

In these formulae, the terms (a_(i), φ_(i)) are optimized so that thecode has a constant energy between 0 and T. The term env(x) is thenonzero amplitude weighting from 0 to T.

It is also possible to choose to bring together the PF frequencies fromthe same side of the broadband code spectrum. The conditions thenbecome: $\left\{ {\begin{matrix}{{{\left( {1 + \frac{2V}{c}} \right)f_{1}} + \frac{2}{T}} \leq {{\left( {1 - \frac{2V}{c} - \frac{2{V_{c}^{\max}}}{c}} \right)f_{m}} - \frac{2}{T}}} & (22) \\{{{{\left( {1 + \frac{2V}{c}} \right)f_{m}} + \frac{2}{T}} \leq {{\left( {1 - \frac{2V}{c} - \frac{2{V_{c}^{\max}}}{c}} \right)f_{M}} - \frac{2}{T}}}\quad} & (23)\end{matrix}{or}\left\{ \begin{matrix}{{{{\left( {1 + \frac{2V}{c} + \frac{2{V_{c}^{\max}}}{c}} \right)f_{m}} + \frac{2}{T}} \leq {{\left( {1 - \frac{2V}{c}} \right)f_{M}} - \frac{2}{T}}}\quad} & (24) \\{{{\left( {1 + \frac{2V}{c} + \frac{2{V_{c}^{\max}}}{c}} \right)f_{M}} + \frac{2}{T}} \leq {{\left( {1 - \frac{2V}{c}} \right)f_{1}} - \frac{2}{T}}} & (25)\end{matrix} \right.} \right.$

What is claimed is:
 1. A process for detecting moving objects by anactive sonar moving at a velocity V, in which a signal of duration T istransmitted, which signal is reverberated by the transmission medium,having a spectral spread due to the actual speed of the sonar and thisreverberated signal is processed by correlation with a set offrequency-shifted copies of the transmission signal in order tocorrespond to the set of Doppler shifts capable of affecting thereverberated signal, characterized in that the transmitted signal isbroadband encoded in order to present a spectrum having a comb-of-linesstructure at successive frequencies f_(i), the interval separating twosuccessive lines f_(i) and f_(i+1) of which is a function of thevelocity V in order to be at least equal to the spectrum spread bysatisfying the formula:${{\left( {1 - \frac{2V}{c}} \right)f_{i + 1}} - \frac{a}{T}} \geq {{\left( {1 + \frac{2V}{c}} \right)f_{i}} + \frac{a}{T}}$

where a is an integer between 1 and 2, c is the speed of acoustic wavesin water and in that the transmission signal also comprises two pulsesat pure frequencies f_(m) and f_(M) intended to make it possible todetect fast moving objects, the echoes from which are located beyond thefrequency band occupied by the reverberated signal, both when recedingand when approaching, these frequencies being given by the equations:${{\left( {1 + \frac{2V}{c} + \frac{2{V_{c}^{\max}}}{c}} \right)f_{m}} + \frac{2}{T}} \leq {{\left( {1 - \frac{2V}{c}} \right)f_{1}} - {\frac{2}{T}\quad {{and}\left( {1 + \frac{2V}{c}} \right)}f_{1}} + \frac{2}{T}} \leq {{\left( {1 - \frac{2V}{c} + \frac{2{v_{c}^{\max}}}{c}} \right)f_{M}} - {\frac{2}{T}.}}$

where V_(c) ^(max) is the maximum velocity of the target.
 2. The processas claimed in claim 1, characterized in that the encoded signal isformed by N pulses, each of which occupies a frequency band B centeredon a frequency f₀, where N is greater than or equal to:$N \cong {\frac{4V\quad T}{c}{\left( {f_{0} + \frac{B}{2}} \right).}}$


3. The process as claimed in claim 1, characterized in that, in orderfor the moving objects, whose speed is approximately equal to one of theblind speeds of the broadband encoded signals, to be detected by thepure-frequency signals, the frequencies f_(m) and f_(M) are chosen tosatisfy, in addition, the equations:$f_{M} = {{q\frac{N}{T}\quad {and}\quad f_{m}} = {\left( {p\quad \pm \quad \frac{\Delta}{2}} \right)\quad \frac{N}{T}}}$

where Δ corresponds to the smallest interval separating the arithmeticseries of the p/q ratio from the series of integers.
 4. The process asclaimed in claim 1, in which f_(m) and f_(M) are chosen so as to satisfythe equations: $\left\{ \begin{matrix}{{{\left( {1\quad + \quad \frac{2\quad V}{c}} \right)\quad f_{1}}\quad + \quad \frac{2}{T}}\quad \leq \quad {{\left( {1\quad - \quad \frac{2\quad V}{c}\quad - \quad \frac{2\quad {V_{c}^{\max}}}{c}} \right)\quad f_{m}}\quad - \quad \frac{2}{T}}} \\{{{\left( {1\quad + \quad \frac{2\quad V}{c}} \right)\quad f_{m}}\quad + \quad \frac{2}{T}}\quad \leq \quad {{\left( {1\quad - \quad \frac{2\quad V}{c}\quad - \quad \frac{2\quad {V_{c}^{\max}}}{c}} \right)\quad f_{M}}\quad - \quad {\frac{2}{T}.}}}\end{matrix} \right.$


5. The process as claimed in claim 1, in which f_(m) and f_(M) arechosen so as to satisfy the equations: $\left\{ \begin{matrix}{{{\left( {1\quad + \quad \frac{2\quad V}{c}\quad + \quad \frac{2\quad {V_{c}^{\max}}}{c}} \right)\quad f_{m}}\quad + \quad \frac{2}{T}}\quad \leq \quad {{\left( {1\quad - \quad \frac{2\quad V}{c}} \right)\quad f_{M}}\quad - \quad \frac{2}{T}}} \\{{{\left( {1\quad + \quad \frac{2\quad V}{c}\quad + \quad \frac{2\quad {V_{c}^{\max}}}{c}} \right)\quad f_{M}}\quad + \quad \frac{2}{T}}\quad \leq \quad {{\left( {1\quad - \quad \frac{2\quad V}{c}} \right)\quad f_{1}}\quad - \quad {\frac{2}{T}.}}}\end{matrix} \right.$


6. The process as claimed in claim 1, characterized in that a towedlinear acoustic antenna is used to receive the reverberated signals. 7.The process as claimed in claim 2, characterized in that, in order forthe moving objects, whose speed is approximately equal to one of theblind speeds of the broadband encoded signals, to be detected by thepure-frequency signals, the frequencies f_(m) and f_(M) are chosen tosatisfy, in addition, the equations:$f_{M} = {{q\frac{N}{T}\quad {and}\quad f_{m}} = {\left( {p\quad \pm \quad \frac{\Delta}{2}} \right)\quad \frac{N}{T}}}$

where Δ corresponds to the smallest interval separating the arithmeticseries of the p/q ratio from the series of integers.
 8. The process asclaimed in claim 2, in which f_(m) and f_(M) are chosen so as to satisfythe equations: $\left\{ \begin{matrix}{{{\left( {1\quad + \quad \frac{2\quad V}{c}} \right)\quad f_{I}}\quad + \quad \frac{2}{T}}\quad \leq \quad {{\left( {1\quad - \quad \frac{2\quad V}{c}\quad - \quad \frac{2\quad {V_{c}^{\max}}}{c}} \right)\quad f_{m}}\quad - \quad \frac{2}{T}}} \\{{{\left( {1\quad + \quad \frac{2\quad V}{c}} \right)\quad f_{m}}\quad + \quad \frac{2}{T}}\quad \leq \quad {{\left( {1\quad - \quad \frac{2\quad V}{c}\quad - \quad \frac{2\quad {V_{c}^{\max}}}{c}} \right)\quad f_{M}}\quad - \quad {\frac{2}{T}.}}}\end{matrix} \right.$


9. The process as claimed in claim 2, in which f_(m) and f_(M) arechosen so as to satisfy the equations: $\left\{ \begin{matrix}{{{\left( {1\quad + \quad \frac{2\quad V}{c}\quad + \quad \frac{2\quad {V_{c}^{\max}}}{c}} \right)\quad f_{m}}\quad + \quad \frac{2}{T}}\quad \leq \quad {{\left( {1\quad - \quad \frac{2\quad V}{c}} \right)\quad f_{M}}\quad - \quad \frac{2}{T}}} \\{{{\left( {1\quad + \quad \frac{2\quad V}{c}\quad + \quad \frac{2\quad {V_{c}^{\max}}}{c}} \right)\quad f_{M}}\quad + \quad \frac{2}{T}}\quad \leq \quad {{\left( {1\quad - \quad \frac{2\quad V}{c}} \right)\quad f_{1}}\quad - \quad {\frac{2}{T}.}}}\end{matrix} \right.$


10. The process as claimed in claim 2, characterized in that a towedlinear acoustic antenna is used to receive the reverberated signals. 11.The process as claimed in claim 3, characterized in that a towed linearacoustic antenna is used to receive the reverberated signals.
 12. Theprocess as claimed in claim 4, characterized in that a towed linearacoustic antenna is used to receive the reverberated signals.
 13. Theprocess as claimed in claim 5, characterized in that a towed linearacoustic antenna is used to receive the reverberated signals.